Chrysler 300 key fob

My 2013 chrysler 300s won't detect my keys. I have to use the nose of the fob to start my car. If the car is running and someone gets in or out then the car says the key has left the vehicle even though the key is in the cup holder. If I lock the doors the only way to unlock the car is with the hidden key in my key fob. Which will set off the alarm. If anyone can help me that'll be great.

Parked in a mall parking lot, when I came out my doors would not unlock with
the key fobs, mine and my husbands, which both have new batteries.
Unlocked with the manual key but the car would not sta...